2D Shallow Water Equations by Composite Schemes

Composite schemes are formed by global composition of several Lax-Wendroff steps followed by a diffusive Lax-Friedrichs or WENO step which filters out the oscillations around shocks typical for the Lax-Wendroff scheme. These schemes are applied to the shallow water equations in 2D. The Lax-Friedrichs composite is also formulated for a trapezoidal mesh, which is necessary in several example problems. The suitability of the composite schemes for the shallow water equations is demonstrated on several examples including the circular dam break problem, the shock focussing problem and supercritical channel flow problems. 1 Introduction The shallow water equations are a system of conservation laws. There are two simple well-known finite difference schemes for conservation laws, Lax-Wendroff (LW) and Lax-Friedrichs (LF). Both of these methods have some drawbacks. The LW scheme is second order accurate but oscillatory close to shocks. The LF scheme is non-oscillatory but also excessively diffu..